Modeling strategic walk-in patients in appointment systems: Equilibrium behavior and capacity allocation

We consider an outpatient clinic with strategic patients who choose between making an appointment with an indirect wait cost (advance patients) and walking in with an inconvenience cost that includes the risk of being rejected and waiting in the clinic (walk-ins). Patients have different indirect waiting costs and show up with some probability. The clinic allocates slots to advance and walk-in patients to minimize the expected blockage of walk-in patients. We characterize the equilibrium behavior of patients and investigate the optimal capacity allocation, for unobservable (patients know the expected waiting time) and observable (patients know their exact waiting time) cases. For the unobservable case, one of the three options is optimal: allocating all slots to advance patients, allocating all slots to walk-ins, or allocating a certain number of slots to advance patients so that only urgent patients would choose the walk-in option. In contrast, for the observable case, no such structure exists. We investigate the value of information numerically. Finally, we develop a simulation platform to examine the effects of model assumptions. We find the optimal capacity allocation for the simulation model to benchmark the performance of the theoretical models and two simple policies. These analyses verify that our models work well in realistic simulations, offering a useful tool in practice. In contrast to the common practice of allocating some slots to walk-ins, our results suggest that the clinics should prefer a system that allocates all slots to advance patients in certain environments due to the strategic behavior of patients.